Problem: Solve for $x$ : $6x^2 - 6x - 72 = 0$
Solution: Dividing both sides by $6$ gives: $ x^2 {-1}x {-12} = 0 $ The coefficient on the $x$ term is $-1$ and the constant term is $-12$ , so we need to find two numbers that add up to $-1$ and multiply to $-12$ The two numbers $3$ and $-4$ satisfy both conditions: $ {3} + {-4} = {-1} $ $ {3} \times {-4} = {-12} $ $(x + {3}) (x {-4}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 3) (x -4) = 0$ $x + 3 = 0$ or $x - 4 = 0$ Thus, $x = -3$ and $x = 4$ are the solutions.